Measurements and Calculations. The Scientific Method A logical approach to solving problems. 1....
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Chapter 2 Measurements and Calculations
Measurements and Calculations. The Scientific Method A logical approach to solving problems. 1. Observation 2. Question/Problem 3. Hypothesis 4. Experiment
The Scientific Method A logical approach to solving problems.
1. Observation 2. Question/Problem 3. Hypothesis 4. Experiment 5.
Analyze 6. Communicate
Slide 3
Observations Use senses to obtain information. State the
facts!! No opinions! Qualitative = descriptive The liquid is clear
blue. Quantitative = numerical The liquid has a density of 1.21
g/mL.
Slide 4
Question/Problem What questions do you have? Does a problem
need to be solved? Formulate a Hypothesis Testable statement or
idea I think If, then
Slide 5
Experiment Test your hypothesis Take measurements Collect data
Analyze Results What does the data tell you? Patterns? Was the
question answered? Problem solved? Develop models & theories
Analysis can lead to more questions, too!!!
Slide 6
Communicate Publish results Confirmation from other
scientists
Slide 7
Measurement All measurements require a number and a unit. The
experiment requires 10.0 mL of ethanol. number = quantity of matter
unit = type of measurement
Slide 8
Significant Figures all certain digits plus the estimated digit
The measurement would be recorded as 1.75 cm. This measurement
contains 3 significant figures. (sig figs) certainestimated
Slide 9
The number of sig figs in a measurement is determined by the
precision of the measuring device. 0cm 1 2 3 4 0cm 40cm 1 2 3 4 3
cm 2.9 cm 2.95 cm 1 cm 1.1 cm 1.10 cm
Slide 10
Not all digits are significant!! Zeros are questionable! 1. All
digits 1-9 are sig. 2. ZEROs a) sandwich zeros = SIG b) at the end
of a number with a decimal point = SIG c) at the end of a number
without a decimal point = NOT SIG d) at the beginning of a number
with a decimal point = NOT SIG
Slide 11
How many sig figs are in the following measurements? 145.7
meters 10.4 kilograms 0.0053 liters 135.20 grams 250 milliliters
250. milliliters 0.0007250450 light years
Slide 12
Handling Measured Numbers and Math: Calculations and Sig Figs
The answer to a math problem cannot be more precise than the
measured numbers used to get the answer. Addition & Subtraction
Rules: Your answer should contain the fewest number of decimal
places as indicated by the measured numbers. Multiplication &
Division Rules: Your answer should contain the fewest number of sig
figs as indicated by the measured numbers.
Slide 13
Examples: 45.25 mL - 43.0 mL 132 g + 11.12 g 36.00 g 12.0 mL
(4.18 cm)(2 cm)
Slide 14
Units of Measurement: SI Base Units Type of Measurement
DefinitionUnit and abbreviation MassAmount of matter present gram,
g VolumeSpace occupied in 3 dimensions Liter, L DistanceSpace
between objects or points Meter, m TimePassage of eventsSecond, s
HeatThermal energyJoule, J TemperatureMolecular motionDegrees
Celsius, C Kelvin, K **Use reference paper for SI prefixes!
Slide 15
Unit Conversions: The Factor Label Method Given Quantity x
Conversion Factor(s) = Answer What is a Conversion Factor? a
fraction that shows how two measurements are numerically equal to
each other.
Slide 16
ex: 1000 milliliters = 1 Liter Conversion Factors would be..
ex: 365.25 days = 1 year Conversion factors would be:
Slide 17
Given Quantity x Conversion factor = Answer Ex: 25.6 mL = ? L
Ex: 2.90 years = ? days
Slide 18
Ex: 78 inches = ? m (1 inch = 2.54 cm) (100 cm = 1 m) Ex: 155
pounds = ? kilograms (1 lb = 454 g) (1000 g = 1 kg)
Slide 19
Ex: 10.0 miles per hour = ? meters per second (1 mile = 5,280
ft) (1 m = 3.28 ft) (1 hr = 60 min) ( 60 s = 1 min)
Slide 20
Derived Measurements measurements that are calculated from
other measurements Area = length x width Volume = length x width x
height Density = mass volume
Slide 21
Examples: 1. What is the area of a rectangle that measures
12.55 cm x 5.85 cm? 2. What is the density of a cube that measures
3.46 cm on each side and has a mass of 44.67 g? 3. The density of a
liquid is 1.15 g/mL. What volume of this liquid would have a mass
of 25.0 grams?
Slide 22
Scientific Notation writing a number as a multiple of 10 x.
1,6000.000000455 1.6 x 10 3 4.55 x 10 -7 Numbers greater than 1
will have a positive exponent. Numbers less than 1 will have a
negative exponent. You must keep one non-zero digit to the left of
the decimal point.
Slide 23
Ex: Write the number in scientific notation. 123,000 km =
_______________ 0.00078 g = ________________ Ex: Write the number
in standard form. 2.4 x 10 -2 L = _______________ 5.02 x 10 5 m =
_______________
Slide 24
Sci. Notation and Sig Figs the 10 x is NOT significant. 4.555 x
10 3 has ____sig figs 1.2 x 10 -4 has ____ sig figs 2.00 x 10 14
has ____ sig figs
Slide 25
Sci. Notation and Your Calculator: Every calculator is slightly
different. When possible use the EE or EXP button. 2.4 x 10 5
TYPE:2.4E5 or 2.4EXP5 Can also use 10 x, but you must put () around
entire number! 2.4 x 10 5 TYPE: (2.4 x 10 x 5)
Slide 26
Examples: 4.23 x 10 12 + 3.22 x 10 11 = 4.55 x 10 18 = 3.2 x 10
3 (5.4 x 10 -7 )(7.80 x 10 -3 ) =
Slide 27
Precision vs. Accuracy in Measurement Precision- how close
multiple measurements are to each other. the reproducibility of a
measurement. Accuracy how close a single measurement is to an
accepted value
Slide 28
Accuracy vs. Precision Accurate? Precise? Accurate ?
Precise?
Slide 29
Percentage Error Describes the accuracy of a measurement. %
error = (accepted value - experimental value) x 100 accepted value
% error can be a positive or a negative answer!!
Slide 30
example: A student measures and calculates the density of a
liquid as 1.35 g/mL. If the density of the liquid is actually 1.42
g/mL, what is the students percent error?
Slide 31
Proportions A proportion represents a relationship between two
measurements. Direct Proportion - as one variable increases, the
second variable increases. Inverse Proportion as one variable
increases, the second variable decreases.